Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-5x-8y &= 9 \\ -8x-9y &= 3\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-8$ and the bottom equation by $5$ $\begin{align*}40x+64y &= -72\\ -40x-45y &= 15\end{align*}$ Add the top and bottom equations. $19y = -57$ Divide both sides by $19$ and reduce as necessary. $y = -3$ Substitute $-3$ for $y$ in the top equation. $-5x-8( -3) = 9$ $-5x+24 = 9$ $-5x = -15$ $x = 3$ The solution is $\enspace x = 3, \enspace y = -3$.